Risk-Sensitive Ordinal Optimization

We consider the problem of risk-sensitive ordinal optimization, which aims to identify the "least risky" system among a finite number of stochastic systems. Each system’s riskiness is assumed to be measured by the probability that the system’s loss exceeds a common threshold. Since the crude Monte Carlo estimator is highly inefficient in estimating rare-event probabilities, conventional ordinal optimization approaches coupled with that estimator show significant performance degradation in this problem, particularly for sufficiently large loss thresholds. To detour this issue, assuming that the parametric form of the underlying distribution is known, we propose to use the tail parameter, a function of distributional parameters, as a surrogate for the loss probability in comparing and ranking systems, which is shown to work well for many well-known distributions. Building upon this observation, we find the optimal computing budget allocation scheme that maximizes the likelihood of identifying the least risky system.